M4471717 Mersenne number exponent details

Residue

Status

L-L

7A57120E1D0D51A0

double-checked

PRP

-unknown-

-unknown-

	Trial Factoring	P-1 Factoring	Combined
Limit	GHz-days	Probability	B1	B2	GHz-days	Probability	GHz-days	Probability	Prob over default TF
Actual	2⁶⁷	6.6449	65.6716%	25000	362500	0.0078	1.3952%	6.6527	66.1506%	0.4789%
PrimeNet	2⁶¹	0.0687	62.2951%	18000	360000	0.0066	2.9457%	0.0753	63.4058%	1.1107%
GPU72	2⁶⁵	1.6315	64.6154%	26000	550000	0.0099	2.0887%	1.6414	65.3545%	0.7391%
Difference	+2	+5.0133	+1.0563%	-1000	-187500	-0.0020	-0.6936%	+5.0113	+0.7961%	+0.7961%

Trial Factoring

P-1 Factoring

Combined

Limit

GHz-days

Probability

GHz-days

Probability

GHz-days

Probability

Prob over default TF

Actual

2⁶⁷

6.6449

65.6716%

25000

362500

0.0078

1.3952%

6.6527

66.1506%

0.4789%

PrimeNet

2⁶¹

0.0687

62.2951%

18000

360000

0.0066

2.9457%

0.0753

63.4058%

1.1107%

GPU72

2⁶⁵

1.6315

64.6154%

26000

550000

0.0099

2.0887%

1.6414

65.3545%

0.7391%

Difference

+5.0133

+1.0563%

-1000

-187500

-0.0020

-0.6936%

+5.0113

+0.7961%

	P-1	GHz-days
exponent	factor	digits	bits*	k	date found	min B1	min B2	min. TF	min. P-1	normal P-1
4471717	228467857412174207561	21	67.631	25545876160340 2² × 5 × 1277293808017	2010-02-13	5	1277293808017	8.7573	12,585	23,506

P-1

GHz-days

exponent

factor

digits

bits*

date found

min B1

min B2

min. TF

min. P-1

normal P-1

4471717

228467857412174207561

67.631

25545876160340
2² × 5 × 1277293808017

2010-02-13

1277293808017

8.7573

12,585

23,506

P-1 results:

										GHz-Days		worth	Factor probability
date	userid	compid	b1	b2	e	stage	factor	digits	bits*	spent	saved	worth	Factor probability
2009-07-24T04:41:00	Carsten Kossendey	durandal	25000	362500		-		-	-	0.008	-	-	1.395%

Trial Factoring results:

			Bits		Factor			GHz-Days		worth
date	userid	compid	from	to	factor	bits*	digits	spent	saved	worth
1998-04-05T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶⁰		-	-	0.034	-	-
2002-06-23T00:00:00	ANONYMOUS	v4_computers	2¹	2⁶¹		-	-	0.069	-	-

ECM factoring results:

Old Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Curves	Complete	FacMiss

New Calculation Method

Total ECM effort:

0.000 GHz-days

Digits	B1	Complete	FacMiss

ECM Summary

B1	B2	factor	curves	GHz-days
		228467857412174207561	1	0.00000e+0

	GHz-Days
date	userid	compid	b1	b2	factor	bits*	curve#	stage#	sigma	numcurves	spent
2010-02-13T06:40:00	alan145	Bear4			228467857412174207561	67.631		1		1	-

Lucas-Lehmer results:

date	userid	compid	res64	spent (GHz-days)
1998-03-31T00:00:00	ANONYMOUS	v4_computers	7A57120E1D0D51A0	0.558
1999-12-01T00:00:00	ANONYMOUS	v4_computers	5FFCB979A8B6AC__	0.558
2001-02-11T00:00:00	ANONYMOUS	v4_computers	7A57120E1D0D51A0	0.558

PRP results:

date

userid

compid

cofactors

res64

PRP

2017-09-20T17:03:39

kkmrkkblmbrbk

Manual testing

228467857412174207561

DE8551DFFF5F31__

2018-02-15T00:01:35

ATH

ec2-1xf

228467857412174207561

DE8551DFFF5F31__

P-1 factor-bounds graph:

X = B1; Y = B2
size of marker relates to size of factor
mouse-over any factor marker (circle) to see additional info
mouse-over any stage bound text to see additional info

B1 = 25000, B2 = 362500 (P-1 stage 2)

B1 = 25000 (P-1 stage 1)

10⁰

10¹

10²

10³

10⁴

10⁵

10⁰

10¹

10²

10³

10⁴

10⁵

10⁶

10⁷

10⁸

10⁹

10¹⁰

10¹¹

10¹²

10¹³

TF factor-bounds graph:

2⁶⁷

2⁶¹

2⁶⁰

2⁵⁰

2⁶⁰

2⁷⁰

2⁸⁰

2⁹⁰

2¹⁰⁰

0M	<	10¹⁰	All tracked exponents
0M	<	2³²	GPU TF range
0M	<	1000M	PrimeNet range
0M	<	193M	low-PrimeNet, low-res
0M	<	385M	low-PrimeNet, high-res
50M	<	146M	PrimeNet wavefront